# Mathematical Diversions

A collection of mathematical miscellany that diverts me from my main research interests. Some of the posts are interesting (to me) mathematical problems with their solutions. Others are mostly recreational things that distracted me at one time or another. The intended audience for posts in this category are my sole self, and so I make no great effort to polish the writing. Do send me an email with questions if you find anything here interesting or confusing.

### Sum space need not be normed

Apologies if this post is shoddily written; I mainly just wanted to record an explicit counterexample before I forget it, and this post …

### Rod and Balls and Finsler (Redux)

In a previous post we discussed a little problem in "almost" Finsler geometry. In this post we will dissect some properties …

### A Rod and Ball Problem (Finsler Geometry)

This post is inspired by: In the diagram a 1 meter rod, initially horizontal, rotates 90-degrees about endpoint B & then translates …

### Jacobi Iteration Method

Summary of the Jacobi iteration method in numerical linear algebra, and some caveats.

### Logical Formulae

Since the COVID-19 crisis and the university moving to online instruction, I've spent too much time programming WeBWorK assignments. …

### Lengths of Parallel Curves

Let's start with something simple: Given a circle with radius $R$, draw a concentric circle with radius 1 larger. How much longer is …

### A Tangent Identity

Here's a slightly non-obvious relation between some angles, that I ran into accidentally. Claim: (angles below given in degrees) \[ …

### An Implicit Assumption about Expectation Values

A short note about an implicit assumption behind the notion of expectation values, and how it relates to economics applications.

### Oscillatory Solutions to the Heat Equation

As we all learned in a first course in PDEs, for "reasonable" initial data $u_0$, the solution to the linear heat equation …

### Some Periodic Functions

Some non-intuitive facts about periodic functions